Mathematica contains a very powerful system of integration. It can do almost any integral that can be done in terms of standard mathematical functions.

Exact symbolic results are usually very desirable when they can be found. In many calculations, however, it is not possible to get symbolic results. In such cases, you must ...

MaxRecursion is an option for functions like NIntegrate and Plot that specifies how many recursive subdivisions can be made.

New method option "PrincipalValue" has been added to the NIntegrate function of the built-in Mathematica kernel. The add-on package is now available on the web at ...

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

These "How tos" give step-by-step instructions for common tasks related to calculus in Mathematica .

NSum[f, {i, i_min, i_max}] gives a numerical approximation to the sum \[Sum]i = i_min i_max f.NSum[f, {i, i_min, i_max, di}] uses a step di in the sum.

Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be ...

NInverseDTFourierTransform[expr, \[Omega], n] gives a numerical approximation to the inverse discrete time Fourier transform of expr evaluated at the integer n, where expr is ...

Compiled is an option for various numerical and plotting functions which specifies whether the expressions they work with should automatically be compiled.